In this question, some equations are solved on the basis of a certain system. On the same basis find out the cor rect answer from amongst the four alternatives for the unsolved equation.
`15xx26=6512`
`29xx36=6923`
`46xx54=?`

कुछ समीकरण एक निश्चित प्रणाली से हल किए गए हैं। उसी आधार पर दिए गए विकल्पों में से सही उत्तर चुनकर लिखिए ?
`15xx26=6512`
`29xx36=6923`
`46xx54=?`

Options

A. 5464
B. 4645
C. 4564
D. 4465

Explanation

To solve the problem, we need to identify the pattern used in the given equations. Let's analyze the provided equations step by step.

### Given Equations:
1. \( 15 \times 26 = 6512 \)
2. \( 29 \times 36 = 6923 \)

### Step 1: Analyze the first equation
For the equation \( 15 \times 26 = 6512 \):
- Break down the numbers:
- \( 15 \) can be represented as \( 1 \) and \( 5 \).
- \( 26 \) can be represented as \( 2 \) and \( 6 \).

Now, if we look at the output \( 6512 \):
- The first digit \( 6 \) comes from \( 2 + 4 \) (where \( 4 \) is the tens digit of \( 15 \)).
- The second digit \( 5 \) comes from \( 5 \) (the units digit of \( 15 \)).
- The third digit \( 1 \) comes from \( 1 \) (the tens digit of \( 15 \)).
- The fourth digit \( 2 \) comes from \( 6 \) (the units digit of \( 26 \)).

### Step 2: Analyze the second equation
For the equation \( 29 \times 36 = 6923 \):
- Break down the numbers:
- \( 29 \) can be represented as \( 2 \) and \( 9 \).
- \( 36 \) can be represented as \( 3 \) and \( 6 \).

Now, if we look at the output \( 6923 \):
- The first digit \( 6 \) comes from \( 3 + 3 \) (where \( 3 \) is the tens digit of \( 29 \)).
- The second digit \( 9 \) comes from \( 9 \) (the units digit of \( 29 \)).
- The third digit \( 2 \) comes from \( 2 \) (the tens digit of \( 29 \)).
- The fourth digit \( 3 \) comes from \( 6 \) (the units digit of \( 36 \)).

### Step 3: Apply the same logic to the unsolved equation
Now, we need to solve for \( 46 \times 54 \):
- Break down the numbers:
- \( 46 \) can be represented as \( 4 \) and \( 6 \).
- \( 54 \) can be represented as \( 5 \) and \( 4 \).

Using the pattern identified:
- The first digit will be \( 5 + 4 = 9 \) (from the tens digit of \( 54 \)).
- The second digit will be \( 6 \) (the units digit of \( 46 \)).
- The third digit will be \( 4 \) (the tens digit of \( 46 \)).
- The fourth digit will be \( 4 \) (the units digit of \( 54 \)).

### Final Answer
Putting it all together, we get:
- The result for \( 46 \times 54 \) is \( 9644 \).

### Conclusion
Thus, the answer to the equation \( 46 \times 54 = ? \) is \( 9644 \).